Information-Theoretic Analysis of Quasi-Stationary Distribution in Domany-Kinzel Automaton
Researchers used matrix-product-state representation to characterize the quasi-stationary distribution of the Domany-Kinzel automaton's bond directed-percolation line, revealing sharp structural changes across phase transitions. The study shows that in the inactive phase, surviving activity concentrates into a single effective cluster encoding just one bit of positional information. This work extends matrix-product-state techniques to absorbing-state systems, enabling new information-theoretic diagnostics beyond traditional observable-based methods.
A new theoretical study characterizes the quasi-stationary distribution (QSD) of the Domany-Kinzel automaton using matrix-product-state representation, which allows direct access to the full conditional probability distribution and information-theoretic measures. The research reveals a sharp spatial transition: the active phase exhibits bulk-like behavior with finite density, while the inactive phase shows surviving activity collapsing into a single flock occupying a vanishing fraction of the chain. The key finding is that throughout the inactive phase, the bipartite mutual information of the QSD equals the entropy of a single binary choice—whether the flock is left or right of a given cut—meaning surviving clusters together encode only one bit of positional information. This approach extends matrix-product-state techniques to the projected eigenvector defining a QSD, providing information-theoretic diagnostics for absorbing-state systems that conventional bulk-observable methods cannot access.
What's missing
The study does not discuss potential experimental realizations or applications of these theoretical findings to physical systems, nor does it compare computational efficiency of this matrix-product-state approach versus existing moment- or sampling-based methods.
What different sources said
- arXiv physicsCenter
Universal Information-Theoretic Structure of the Quasi-Stationary Domany--Kinzel Automaton
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